Problem: The sum of two numbers is $51$, and their difference is $5$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 51}$ ${x-y = 5}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 56 $ $ x = \dfrac{56}{2} $ ${x = 28}$ Now that you know ${x = 28}$ , plug it back into $ {x+y = 51}$ to find $y$ ${(28)}{ + y = 51}$ ${y = 23}$ You can also plug ${x = 28}$ into $ {x-y = 5}$ and get the same answer for $y$ ${(28)}{ - y = 5}$ ${y = 23}$ Therefore, the larger number is $28$, and the smaller number is $23$.